Hindawi Publishing CorporationEURASIP Journal on Advances in Signal ProcessingVolume 2010, Article ID 381465, 15 pagesdoi:10.1155/2010/381465

Review Article

A Review on Spectrum Sensing for Cognitive Radio:Challenges and Solutions

Yonghong Zeng, Ying-Chang Liang, Anh Tuan Hoang, and Rui Zhang

Institute for Infocomm Research, A∗STAR, Singapore 138632

Correspondence should be addressed to Yonghong Zeng, yhzeng@i2r.a-star.edu.sg

Received 13 May 2009; Accepted 9 October 2009

Academic Editor: Jinho Choi

Copyright © 2010 Yonghong Zeng et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Cognitive radio is widely expected to be the next Big Bang in wireless communications. Spectrum sensing, that is, detecting thepresence of the primary users in a licensed spectrum, is a fundamental problem for cognitive radio. As a result, spectrum sensinghas reborn as a very active research area in recent years despite its long history. In this paper, spectrum sensing techniques from theoptimal likelihood ratio test to energy detection, matched filtering detection, cyclostationary detection, eigenvalue-based sensing,joint space-time sensing, and robust sensing methods are reviewed. Cooperative spectrum sensing with multiple receivers is alsodiscussed. Special attention is paid to sensing methods that need little prior information on the source signal and the propagationchannel. Practical challenges such as noise power uncertainty are discussed and possible solutions are provided. Theoretical analysison the test statistic distribution and threshold setting is also investigated.

1. Introduction

It was shown in a recent report [1] by the USA FederalCommunications Commission (FCC) that the conventionalfixed spectrum allocation rules have resulted in low spectrumusage efficiency in almost all currently deployed frequencybands. Measurements in other countries also have shownsimilar results [2]. Cognitive radio, first proposed in [3], isa promising technology to fully exploit the under-utilizedspectrum, and consequently it is now widely expected to bethe next Big Bang in wireless communications. There havebeen tremendous academic researches on cognitive radios,for example, [4, 5], as well as application initiatives, such asthe IEEE 802.22 standard on wireless regional area network(WRAN) [6, 7] and the Wireless Innovation Alliance [8]including Google and Microsoft as members, which advocateto unlock the potential in the so-called “White Spaces” inthe television (TV) spectrum. The basic idea of a cognitiveradio is spectral reusing or spectrum sharing, which allowsthe secondary networks/users to communicate over thespectrum allocated/licensed to the primary users when theyare not fully utilizing it. To do so, the secondary usersare required to frequently perform spectrum sensing, that

is, detecting the presence of the primary users. Wheneverthe primary users become active, the secondary users haveto detect the presence of them with a high probabilityand vacate the channel or reduce transmit power withincertain amount of time. For example, for the upcoming IEEE802.22 standard, it is required for the secondary users todetect the TV and wireless microphone signals and vacantthe channel within two seconds once they become active.Furthermore, for TV signal detection, it is required to achieve90% probability of detection and 10% probability of falsealarm at signal-to-noise ratio (SNR) level as low as −20 dB.

There are several factors that make spectrum sensingpractically challenging. First, the required SNR for detectionmay be very low. For example, even if a primary transmitteris near a secondary user (the detection node), the transmittedsignal of the primary user can be deep faded such thatthe primary signal’s SNR at the secondary receiver is wellbelow −20 dB. However, the secondary user still needsto detect the primary user and avoid using the channelbecause it may strongly interfere with the primary receiverif it transmits. A practical scenario of this is a wirelessmicrophone operating in TV bands, which only transmitswith a power less than 50 mW and a bandwidth less than

2 EURASIP Journal on Advances in Signal Processing

200 KHz. If a secondary user is several hundred metersaway from the microphone device, the received SNR maybe well below −20 dB. Secondly, multipath fading and timedispersion of the wireless channels complicate the sensingproblem. Multipath fading may cause the signal power tofluctuate as much as 30 dB. On the other hand, unknowntime dispersion in wireless channels may turn the coherentdetection unreliable. Thirdly, the noise/interference levelmay change with time and location, which yields the noisepower uncertainty issue for detection [9–12].

Facing these challenges, spectrum sensing has reborn asa very active research area over recent years despite its longhistory. Quite a few sensing methods have been proposed,including the classic likelihood ratio test (LRT) [13], energydetection (ED) [9, 10, 13, 14], matched filtering (MF) detec-tion [10, 13, 15], cyclostationary detection (CSD) [16–19],and some newly emerging methods such as eigenvalue-basedsensing [6, 20–25], wavelet-based sensing [26], covariance-based sensing [6, 27, 28], and blindly combined energydetection [29]. These methods have different requirementsfor implementation and accordingly can be classified intothree general categories: (a) methods requiring both sourcesignal and noise power information, (b) methods requiringonly noise power information (semiblind detection), and(c) methods requiring no information on source signal ornoise power (totally blind detection). For example, LRT,MF, and CSD belong to category A; ED and wavelet-basedsensing methods belong to category B; eigenvalue-basedsensing, covariance-based sensing, and blindly combinedenergy detection belong to category C. In this paper, wefocus on methods in categories B and C, although someother methods in category A are also discussed for the sakeof completeness. Multiantenna/receiver systems have beenwidely deployed to increase the channel capacity or improvethe transmission reliability in wireless communications. Inaddition, multiple antennas/receivers are commonly usedto form an array radar [30, 31] or a multiple-inputmultiple-output (MIMO) radar [32, 33] to enhance theperformance of range, direction, and/or velocity estimations.Consequently, MIMO techniques can also be applied toimprove the performance of spectrum sensing. Therefore,in this paper we assume a multi-antenna system model ingeneral, while the single-antenna system is treated as a specialcase.

When there are multiple secondary users/receivers dis-tributed at different locations, it is possible for them tocooperate to achieve higher sensing reliability. There arevarious sensing cooperation schemes in the current literature[34–44]. In general, these schemes can be classified into twocategories: (A) data fusion: each user sends its raw data orprocessed data to a specific user, which processes the datacollected and then makes the final decision; (B) decisionfusion: multiple users process their data independently andsend their decisions to a specific user, which then makes thefinal decision.

In this paper, we will review various spectrum sensingmethods from the optimal LRT to practical joint space-timesensing, robust sensing, and cooperative sensing and discusstheir advantages and disadvantages. We will pay special

attention to sensing methods with practical applicationpotentials. The focus of this paper is on practical sensingalgorithm designs; for other aspects of spectrum sensing incognitive radio, the interested readers may refer to otherresources like [45–52].

The rest of this paper is organized as follows. Thesystem model for the general setup with multiple receiversfor sensing is given in Section 2. The optimal LRT-basedsensing due to the Neyman-Pearson theorem is reviewedin Section 3. Under some special conditions, it is shownthat the LRT becomes equivalent to the estimator-correlatordetection, energy detection, or matched filtering detection.The Bayesian method and the generalized LRT for sensingare discussed in Section 4. Detection methods based onthe spatial correlations among multiple received signals arediscussed in Section 5, where optimally combined energydetection and blindly combined energy detection are shownto be optimal under certain conditions. Detection methodscombining both spatial and time correlations are reviewed inSection 6, where the eigenvalue-based and covariance-baseddetections are discussed in particular. The cyclostationarydetection, which exploits the statistical features of the pri-mary signals, is reviewed in Section 7. Cooperative sensingis discussed in Section 8. The impacts of noise uncertaintyand noise power estimation to the sensing performanceare analyzed in Section 9. The test statistic distribution andthreshold setting for sensing are reviewed in Section 10,where it is shown that the random matrix theory is veryuseful for the related study. The robust spectrum sensingto deal with uncertainties in source signal and/or noisepower knowledge is reviewed in Section 11, with specialemphasis on the robust versions of LRT and matched filteringdetection methods. Practical challenges and future researchdirections for spectrum sensing are discussed in Section 12.Finally, Section 13 concludes the paper.

2. System Model

We assume that there are M ≥ 1 antennas at the receiver.These antennas can be sufficiently close to each other toform an antenna array or well separated from each other.We assume that a centralized unit is available to process thesignals from all the antennas. The model under considerationis also applicable to the multinode cooperative sensing [34–44, 53], if all nodes are able to send their observed signals toa central node for processing. There are two hypotheses: H0,signal absent, and H1, signal present. The received signal atantenna/receiver i is given by

H0 : xi(n) = ηi(n),

H1 : xi(n) = si(n) + ηi(n), i = 1, . . . ,M.(1)

In hypothesis H1, si(n) is the received source signal atantenna/receiver i, which may include the channel multipathand fading effects. In general, si(n) can be expressed as

si(n) =K∑

k=1

qik∑

l=0

hik(l)sk(n− l), (2)

EURASIP Journal on Advances in Signal Processing 3

where K denotes the number of primary user/antennasignals, sk(n) denotes the transmitted signal from primaryuser/antenna k, hik(l) denotes the propagation channelcoefficient from the kth primary user/antenna to the ithreceiver antenna, and qik denotes the channel order for hik.It is assumed that the noise samples ηi(n)’s are independentand identically distributed (i.i.d) over both n and i. Forsimplicity, we assume that the signal, noise, and channelcoefficients are all real numbers.

The objective of spectrum sensing is to make a decisionon the binary hypothesis testing (choose H0 or H1) based onthe received signal. If the decision is H1, further informationsuch as signal waveform and modulation schemes may beclassified for some applications. However, in this paper, wefocus on the basic binary hypothesis testing problem. Theperformance of a sensing algorithm is generally indicated bytwo metrics: probability of detection, Pd, which defines, atthe hypothesis H1, the probability of the algorithm correctlydetecting the presence of the primary signal; and probabilityof false alarm, Pf a, which defines, at the hypothesis H0,the probability of the algorithm mistakenly declaring thepresence of the primary signal. A sensing algorithm is called“optimal” if it achieves the highest Pd for a given Pf a with afixed number of samples, though there could be other criteriato evaluate the performance of a sensing algorithm.

Stacking the signals from the M antennas/receivers yieldsthe following M × 1 vectors:

x(n) =[x1(n) · · · xM(n)

]T,

s(n) =[s1(n) · · · sM(n)

]T,

η(n) =[η1(n) · · · ηM(n)

]T.

(3)

The hypothesis testing problem based on N signal samples isthen obtained as

H0 : x(n) = η(n),

H1 : x(n) = s(n) + η(n), n = 0, . . . ,N − 1.(4)

3. Neyman-Pearson Theorem

The Neyman-Pearson (NP) theorem [13, 54, 55] states that,for a given probability of false alarm, the test statistic thatmaximizes the probability of detection is the likelihood ratiotest (LRT) defined as

TLRT(x) = p(x |H1)p(x |H0)

, (5)

where p(·) denotes the probability density function (PDF),and x denotes the received signal vector that is the aggre-gation of x(n), n = 0, 1, . . . ,N − 1. Such a likelihood ratiotest decides H1 when TLRT(x) exceeds a threshold γ, and H0

otherwise.The major difficulty in using the LRT is its requirements

on the exact distributions given in (5). Obviously, thedistribution of random vector x under H1 is related to the

source signal distribution, the wireless channels, and thenoise distribution, while the distribution of x under H0 isrelated to the noise distribution. In order to use the LRT, weneed to obtain the knowledge of the channels as well as thesignal and noise distributions, which is practically difficult torealize.

If we assume that the channels are flat-fading, and thereceived source signal sample si(n)’s are independent over n,the PDFs in LRT are decoupled as

p(x |H1) =N−1∏

n=0

p(x(n) |H1),

p(x |H0) =N−1∏

n=0

p(x(n) |H0).

(6)

If we further assume that noise and signal samples are bothGaussian distributed, that is, η(n) ∼ N (0, σ2

η I) and s(n) ∼N (0, Rs), the LRT becomes the estimator-correlator (EC)[13] detector for which the test statistic is given by

TEC(x) =N−1∑

n=0

xT(n)Rs

(Rs + σ2

η I)−1

x(n). (7)

From (4), we see that Rs(Rs + 2σ2η I)−1x(n) is actually the

minimum-mean-squared-error (MMSE) estimation of thesource signal s(n). Thus, TEC(x) in (7) can be seen as thecorrelation of the observed signal x(n) with the MMSEestimation of s(n).

The EC detector needs to know the source signalcovariance matrix Rs and noise power σ2

η . When the signalpresence is unknown yet, it is unrealistic to require the sourcesignal covariance matrix (related to unknown channels) fordetection. Thus, if we further assume that Rs = σ2

s I, the ECdetector in (7) reduces to the well-known energy detector(ED) [9, 14] for which the test statistic is given as follows (bydiscarding irrelevant constant terms):

TED(x) =N−1∑

n=0

xT(n)x(n). (8)

Note that for the multi-antenna/receiver case, TED is actuallythe summation of signals from all antennas, which is astraightforward cooperative sensing scheme [41, 56, 57]. Ingeneral, the ED is not optimal if Rs is non-diagonal.

If we assume that noise is Gaussian distributed andsource signal s(n) is deterministic and known to the receiver,which is the case for radar signal processing [32, 33, 58], it iseasy to show that the LRT in this case becomes the matchedfiltering-based detector, for which the test statistic is

TMF(x) =N−1∑

n=0

sT(n)x(n). (9)

4. Bayesian Method and the GeneralizedLikelihood Ratio Test

In most practical scenarios, it is impossible to know thelikelihood functions exactly, because of the existence of

4 EURASIP Journal on Advances in Signal Processing

uncertainty about one or more parameters in these func-tions. For instance, we may not know the noise power σ2

η

and/or source signal covariance Rs. Hypothesis testing in thepresence of uncertain parameters is known as “composite”hypothesis testing. In classic detection theory, there are twomain approaches to tackle this problem: the Bayesian methodand the generalized likelihood ratio test (GLRT).

In the Bayesian method [13], the objective is to eval-uate the likelihood functions needed in the LRT throughmarginalization, that is,

p(x |H0) =∫p(x |H0,Θ0)p(Θ0 |H0)dΘ0, (10)

where Θ0 represents all the unknowns when H0 is true. Notethat the integration operation in (10) should be replacedwith a summation if the elements in Θ0 are drawn from adiscrete sample space. Critically, we have to assign a priordistribution p(Θ0 | H0) to the unknown parameters. Inother words, we need to treat these unknowns as randomvariables and use their known distributions to express ourbelief in their values. Similarly, p(x | H1) can be defined.The main drawbacks of the Bayesian approach are listed asfollows.

(1) The marginalization operation in (10) is often nottractable except for very simple cases.

(2) The choice of prior distributions affects the detectionperformance dramatically and thus it is not a trivialtask to choose them.

To make the LRT applicable, we may estimate theunknown parameters first and then use the estimatedparameters in the LRT. Known estimation techniques couldbe used for this purpose [59]. However, there is one majordifference from the conventional estimation problem wherewe know that signal is present, while in the case of spectrumsensing we are not sure whether there is source signal or not(the first priority here is the detection of signal presence). Atdifferent hypothesis (H0 or H1), the unknown parametersare also different.

The GLRT is one efficient method [13, 55] to resolve theabove problem, which has been used in many applications,for example, radar and sonar signal processing. For thismethod, the maximum likelihood (ML) estimation of theunknown parameters under H0 and H1 is first obtained as

Θ0 = arg maxΘ0

p(x |H0,Θ0),

Θ1 = arg maxΘ1

p(x |H1,Θ1),(11)

where Θ0 and Θ1 are the set of unknown parameters underH0 and H1, respectively. Then, the GLRT statistic is formedas

TGLRT(x) =p(

x | Θ1, H1

)

p(

x | Θ0, H0

) . (12)

Finally, the GLRT decides H1 if TGLRT(x) > γ, where γ is athreshold, and H0 otherwise.

It is not guaranteed that the GLRT is optimal orapproaches to be optimal when the sample size goes toinfinity. Since the unknown parameters in Θ0 and Θ1 arehighly dependent on the noise and signal statistical models,the estimations of them could be vulnerable to the modelingerrors. Under the assumption of Gaussian distributed sourcesignals and noises, and flat-fading channels, some efficientspectrum sensing methods based on the GLRT can be foundin [60].

5. Exploiting Spatial Correlation ofMultiple Received Signals

The received signal samples at different antennas/receiversare usually correlated, because all si(n)’s are generated fromthe same source signal sk(n)’s. As mentioned previously, theenergy detection defined in (8) is not optimal for this case.Furthermore, it is difficult to realize the LRT in practice.Hence, we consider suboptimal sensing methods as follows.

If M > 1, K = 1, and assuming that the propagationchannels are flat-fading (qik = 0, ∀i, k) and known to thereceiver, the energy at different antennas can be coherentlycombined to obtain a nearly optimal detection [41, 43,57]. This is also called maximum ratio combining (MRC).However, in practice, the channel coefficients are unknownat the receiver. As a result, the coherent combining may notbe applicable and the equal gain combining (EGC) is used inpractice [41, 57], which is the same as the energy detectiondefined in (8).

In general, we can choose a matrix B with M rows tocombine the signals from all antennas as

z(n) = BTx(n), n = 0, 1, . . . ,N − 1. (13)

The combining matrix should be chosen such that theresultant signal has the largest SNR. It is obvious that theSNR after combining is

Γ(B) =E[∥∥BTs(n)

∥∥2]

E[∥∥BTη(n)

∥∥2] , (14)

where E(·) denotes the mathematical expectation. Hence,the optimal combining matrix should maximize the valueof function Γ(B). Let Rs = E[s(n)sT(n)] be the statisticalcovariance matrix of the primary signals. It can be verifiedthat

Γ(B) = Tr(

BTRsB)

σ2ηTr(BTB)

, (15)

where Tr(·) denotes the trace of a matrix. Let λmax be themaximum eigenvalue of Rs and let β1 be the correspondingeigenvector. It can be proved that the optimal combiningmatrix degrades to the vector β1 [29].

Upon substituting β1 into (13), the test statistic for theenergy detection becomes

TOCED(x) = 1N

N−1∑

n=0

‖z(n)‖2. (16)

EURASIP Journal on Advances in Signal Processing 5

The resulting detection method is called optimally combinedenergy detection (OCED) [29]. It is easy to show that this teststatistic is better than TED(x) in terms of SNR.

The OCED needs an eigenvector of the received sourcesignal covariance matrix, which is usually unknown. Toovercome this difficulty, we provide a method to estimatethe eigenvector using the received signal samples only.Considering the statistical covariance matrix of the signaldefined as

Rx = E[

x(n)xT(n)]

, (17)

we can verify that

Rx = Rs + σ2η IM. (18)

Since Rx and Rs have the same eigenvectors, the vector β1is also the eigenvector of Rx corresponding to its maximumeigenvalue. However, in practice, we do not know thestatistical covariance matrix Rx either, and therefore wecannot obtain the exact vector β1. An approximation of thestatistical covariance matrix is the sample covariance matrixdefined as

Rx(N) = 1N

N−1∑

n=0

x(n)xT(n). (19)

Let β1 (normalized to ‖β1‖2 = 1) be the eigenvector of the

sample covariance matrix corresponding to its maximum

eigenvalue. We can replace the combining vector β1 by β1,that is,

z(n) = βT

1 x(n). (20)

Then, the test statistics for the resulting blindly combinedenergy detection (BCED) [29] becomes

TBCED(x) = 1N

N−1∑

n=0

∣∣z(n)∣∣2. (21)

It can be verified that

TBCED(x) = 1N

N−1∑

n=0

βT

1 x(n)xT(n)β1

= βT

1 Rx(N)β1

= λmax(N),

(22)

where λmax(N) is the maximum eigenvalue of Rx(N). Thus,TBCED(x) can be taken as the maximum eigenvalue of thesample covariance matrix. Note that this test is a special caseof the eigenvalue-based detection (EBD) [20–25].

6. Combining Space and Time Correlation

In addition to being spatially correlated, the received signalsamples are usually correlated in time due to the followingreasons.

(1) The received signal is oversampled. Let Δ0 be theNyquist sampling period of continuous-time signal sc(t) andlet sc(nΔ0) be the sampled signal based on the Nyquistsampling rate. Thanks to the Nyquist theorem, the signalsc(t) can be expressed as

sc(t) =∞∑

n=−∞sc(nΔ0)g(t − nΔ0), (23)

where g(t) is an interpolation function. Hence, the signalsamples s(n) = sc(nΔs) are only related to sc(nΔ0), whereΔs is the actual sampling period. If the sampling rate atthe receiver is Rs = 1/Δs > 1/Δ0, that is, Δs < Δ0, thens(n) = sc(nΔs) must be correlated over n. An example ofthis is the wireless microphone signal specified in the IEEE802.22 standard [6, 7], which occupies about 200 KHz in a6-MHz TV band. In this example, if we sample the receivedsignal with sampling rate no lower than 6 MHz, the wirelessmicrophone signal is actually oversampled and the resultingsignal samples are highly correlated in time.

(2) The propagation channel is time-dispersive. In thiscase, the received signal can be expressed as

sc(t) =∫∞

−∞h(τ)s0(t − τ)dτ, (24)

where s0(t) is the transmitted signal and h(t) is the responseof the time-dispersive channel. Since the sampling period Δsis usually very small, the integration (24) can be approxi-mated as

sc(t) ≈ Δs

∞∑

k=−∞h(kΔs)s0(t − kΔs). (25)

Hence,

sc(nΔs) ≈ Δs

J1∑

k=J0h(kΔs)s0((n− k)Δs), (26)

where [J0Δs, J1Δs] is the support of the channel responseh(t), with h(t) = 0 for t /∈ [J0Δs, J1Δs]. For time-dispersivechannels, J1 > J0 and thus even if the original signal sampless0(nΔs)’s are i.i.d., the received signal samples sc(nΔs)’s arecorrelated.

(3) The transmitted signal is correlated in time. In thiscase, even if the channel is flat-fading and there is nooversampling at the receiver, the received signal samples arecorrelated.

The above discussions suggest that the assumption ofindependent (in time) received signal samples may be invalidin practice, such that the detection methods relying on thisassumption may not perform optimally. However, additionalcorrelation in time may not be harmful for signal detection,while the problem is how we can exploit this property. Forthe multi-antenna/receiver case, the received signal samplesare also correlated in space. Thus, to use both the spaceand time correlations, we may stack the signals from the M

6 EURASIP Journal on Advances in Signal Processing

antennas and over L sampling periods all together and definethe corresponding ML× 1 signal/noise vectors:

xL(n) =[x1(n) · · · xM(n) x1(n− 1) · · · xM(n− 1)

· · · x1(n− L + 1) · · · xM(n− L + 1)]T

(27)

sL(n) =[s1(n) · · · sM(n) s1(n− 1) · · · sM(n−1)

· · · s1(n− L + 1) · · · sM(n− L + 1)]T

(28)

ηL(n) =[η1(n) · · · ηM(n) η1(n− 1) · · · ηM(n− 1)

· · · η1(n− L + 1) · · · ηM(n− L + 1)]T.(29)

Then, by replacing x(n) by xL(n), we can directly extend thepreviously introduced OCED and BCED methods to incor-porate joint space-time processing. Similarly, the eigenvalue-based detection methods [21–24] can also be modified towork for correlated signals in both time and space. Anotherapproach to make use of space-time signal correlation isthe covariance based detection [27, 28, 61] briefly describedas follows. Defining the space-time statistical covariancematrices for the signal and noise as

RL,x = E[

xL(n)xTL (n)]

,

RL,s = E[

sL(n)sTL (n)]

,(30)

respectively, we can verify that

RL,x = RL,s + σ2η IL. (31)

If the signal is not present, RL,s = 0, and thus the off-diagonalelements in RL,x are all zeros. If there is a signal and the signalsamples are correlated, RL,s is not a diagonal matrix. Hence,the nonzero off-diagonal elements of RL,x can be used forsignal detection.

In practice, the statistical covariance matrix can only becomputed using a limited number of signal samples, whereRL,x can be approximated by the sample covariance matrixdefined as

RL,x(N) = 1N

N−1∑

n=0

xL(n)xTL (n). (32)

Based on the sample covariance matrix, we could develop thecovariance absolute value (CAV) test [27, 28] defined as

TCAV(x) = 1ML

ML∑

n=1

ML∑

m=1

|rnm(N)|, (33)

where rnm(N) denotes the (n,m)th element of the samplecovariance matrix RL,x(N).

There are other ways to utilize the elements in thesample covariance matrix, for example, the maximum valueof the nondiagonal elements, to form different test statistics.

Especially, when we have some prior information on thesource signal correlation, we may choose a correspondingsubset of the elements in the sample covariance matrix toform a more efficient test.

Another effective usage of the covariance matrix forsensing is the eigenvalue based detection (EBD) [20–25],which uses the eigenvalues of the covariance matrix as teststatistics.

7. Cyclostationary Detection

Practical communication signals may have special statisti-cal features. For example, digital modulated signals havenonrandom components such as double sidedness due tosinewave carrier and keying rate due to symbol period. Suchsignals have a special statistical feature called cyclostation-arity, that is, their statistical parameters vary periodicallyin time. This cyclostationarity can be extracted by thespectral-correlation density (SCD) function [16–18]. For acyclostationary signal, its SCD function takes nonzero valuesat some nonzero cyclic frequencies. On the other hand, noisedoes not have any cyclostationarity at all; that is, its SCDfunction has zero values at all non-zero cyclic frequencies.Hence, we can distinguish signal from noise by analyzing theSCD function. Furthermore, it is possible to distinguish thesignal type because different signals may have different non-zero cyclic frequencies.

In the following, we list cyclic frequencies for somesignals of practical interest [17, 18].

(1) Analog TV signal: it has cyclic frequencies at mul-tiples of the TV-signal horizontal line-scan rate(15.75 KHz in USA, 15.625 KHz in Europe).

(2) AM signal: x(t) = a(t) cos(2π fct + φ0). It has cyclicfrequencies at ±2 fc.

(3) PM and FM signal: x(t) = cos(2π fct+φ(t)). It usuallyhas cyclic frequencies at ±2 fc. The characteristics ofthe SCD function at cyclic frequency±2 fc depend onφ(t).

(4) Digital-modulated signals are as follows

(a) Amplitude-Shift Keying: x(t) = [∑∞

n=−∞ anp(t− nΔs − t0)] cos(2π fct + φ0). It has cyclicfrequencies at k/Δs, k /= 0 and±2 fc +k/Δs, k =0,±1,±2, . . . .

(b) Phase-Shift Keying: x(t) = cos[2π fct +∑∞n=−∞ anp(t−nΔs−t0)]. For BPSK, it has cyclic

frequencies at k/Δs, k /= 0, and±2 fc+k/Δs, k =0,±1,±2, . . . . For QPSK, it has cycle frequenciesat k/Δs, k /= 0.

When source signal x(t) passes through a wirelesschannel, the received signal is impaired by the unknownpropagation channel. In general, the received signal can bewritten as

y(t) = x(t)⊗ h(t), (34)

EURASIP Journal on Advances in Signal Processing 7

where ⊗ denotes the convolution, and h(t) denotes thechannel response. It can be shown that the SCD function ofy(t) is

Sy(f) = H

(f +

α

2

)H∗(f − α

2

)Sx(f), (35)

where ∗ denotes the conjugate, α denotes the cyclic fre-quency for x(t), H( f ) is the Fourier transform of thechannel h(t), and Sx( f ) is the SCD function of x(t). Thus,the unknown channel could have major impacts on thestrength of SCD at certain cyclic frequencies.

Although cyclostationary detection has certain advan-tages (e.g., robustness to uncertainty in noise power andpropagation channel), it also has some disadvantages: (1) itneeds a very high sampling rate; (2) the computation of SCDfunction requires large number of samples and thus highcomputational complexity; (3) the strength of SCD couldbe affected by the unknown channel; (4) the sampling timeerror and frequency offset could affect the cyclic frequencies.

8. Cooperative Sensing

When there are multiple users/receivers distributed in differ-ent locations, it is possible for them to cooperate to achievehigher sensing reliability, thus resulting in various cooper-ative sensing schemes [34–44, 53, 62]. Generally speaking,if each user sends its observed data or processed data to aspecific user, which jointly processes the collected data andmakes a final decision, this cooperative sensing scheme iscalled data fusion. Alternatively, if multiple receivers processtheir observed data independently and send their decisions toa specific user, which then makes a final decision, it is calleddecision fusion.

8.1. Data Fusion. If the raw data from all receivers are sentto a central processor, the previously discussed methodsfor multi-antenna sensing can be directly applied. However,communication of raw data may be very expensive forpractical applications. Hence, in many cases, users only sendprocessed/compressed data to the central processor.

A simple cooperative sensing scheme based on the energydetection is the combined energy detection. For this scheme,each user computes its received source signal (including thenoise) energy as TED,i = (1/N)

∑N−1n=0 |xi(n)|2 and sends it to

the central processor, which sums the collected energy valuesusing a linear combination (LC) to obtain the following teststatistic:

TLC(x) =M∑

i=1

giTED,i, (36)

where gi is the combining coefficient, with gi ≥ 0 and∑Mi=1 gi = 1. If there is no information on the source signal

power received by each user, the EGC can be used, that is,gi = 1/M for all i. If the source signal power received byeach user is known, the optimal combining coefficients can

be found [38, 43]. For the low-SNR case, it can be shown [43]that the optimal combining coefficients are given by

gi = σ2i∑M

k=1 σ2k

, i = 1, . . . ,M, (37)

where σ2i is the received source signal (excluding the noise)

power of user i.A fusion scheme based on the CAV is given in [53],

which has the capability to mitigate interference and noiseuncertainty.

8.2. Decision Fusion. In decision fusion, each user sends itsone-bit or multiple-bit decision to a central processor, whichdeploys a fusion rule to make the final decision. Specifically, ifeach user only sends one-bit decision (“1” for signal presentand “0” for signal absent) and no other information isavailable at the central processor, some commonly adopteddecision fusion rules are described as follows [42].

(1) “Logical-OR (LO)” Rule: If one of the decisions is “1,”the final decision is “1.” Assuming that all decisionsare independent, then the probability of detectionand probability of false alarm of the final decision arePd = 1−∏M

i=1(1−Pd,i) and Pf a = 1−∏Mi=1(1−Pf a,i),

respectively, where Pd,i and Pf a,i are the probabilityof detection and probability of false alarm for user i,respectively.

(2) “Logical-AND (LA)” Rule: If and only if all decisionsare “1,” the final decision is “1.” The probability ofdetection and probability of false alarm of the finaldecision are Pd = ∏M

i=1Pd,i and Pf a =∏M

i=1Pf a,i,respectively.

(3) “K out of M” Rule: If and only if K decisionsor more are “1”s, the final decision is “1.” Thisincludes “Logical-OR (LO)” (K = 1), “Logical-AND(LA)” (K = M), and “Majority” (K = �M/2�) asspecial cases [34]. The probability of detection andprobability of false alarm of the final decision are

Pd =M−K∑

i=0

⎛⎝

M

K + i

⎞⎠(1− Pd,i

)M−K−i

× (1− Pd,i)K+i,

Pf a =M−K∑

i=0

⎛⎝

M

K + i

⎞⎠(

1− Pf a,i

)M−K−i

×(

1− Pf a,i

)K+i,

(38)

respectively.

Alternatively, each user can send multiple-bit decisionsuch that the central processor gets more information tomake a more reliable decision. A fusion scheme based onmultiple-bit decisions is shown in [41]. In general, there is atradeoff between the number of decision bits and the fusion

8 EURASIP Journal on Advances in Signal Processing

reliability. There are also other fusion rules that may requireadditional information [34, 63].

Although cooperative sensing can achieve better perfor-mance, there are some issues associated with it. First, reliableinformation exchanges among the cooperating users mustbe guaranteed. In an ad hoc network, this is by no meansa simple task. Second, most data fusion methods in literatureare based on the simple energy detection and flat-fadingchannel model, while more advanced data fusion algorithmssuch as cyclostationary detection, space-time combining,and eigenvalue-based detection, over more practical prop-agation channels need to be further investigated. Third,existing decision fusions have mostly assumed that decisionsof different users are independent, which may not be truebecause all users actually receive signals from some commonsources. At last, practical fusion algorithms should be robustto data errors due to channel impairment, interference, andnoise.

9. Noise Power Uncertainty and Estimation

For many detection methods, the receiver noise power isassumed to be known a priori, in order to form the teststatistic and/or set the test threshold. However, the noisepower level may change over time, thus yielding the so-called noise uncertainty problem. There are two types ofnoise uncertainty: receiver device noise uncertainty andenvironment noise uncertainty. The receiver device noiseuncertainty comes from [9–11]: (a) nonlinearity of receivercomponents and (b) time-varying thermal noise in thesecomponents. The environment noise uncertainty is causedby transmissions of other users, either unintentionally orintentionally. Because of the noise uncertainty, in practice,it is very difficult to obtain the accurate noise power.

Let the estimated noise power be σ2η = ασ2

η , where α iscalled the noise uncertainty factor. The upper bound on α(in dB scale) is then defined as

B = sup{

10 log10α}

, (39)

where B is called the noise uncertainty bound. It is usuallyassumed that α in dB scale, that is, 10 log10α, is uniformlydistributed in the interval [−B,B] [10]. In practice, thenoise uncertainty bound of a receiving device is normallybelow 2 dB [10, 64], while the environment/interferencenoise uncertainty can be much larger [10]. When there isnoise uncertainty, it is known that the energy detection is noteffective [9–11, 64].

To resolve the noise uncertainty problem, we need toestimate the noise power in real time. For the multi-antennacase, if we know that the number of active primary signals,K , is smaller than M, the minimum eigenvalue of the samplecovariance matrix can be a reasonable estimate of the noisepower. If we further assume to know the difference M −K , the average of the M − K smallest eigenvalues can beused as a better estimate of the noise power. Accordingly,instead of comparing the test statistics with an assumed noisepower, we can compare them with the estimated noise powerfrom the sample covariance matrix. For example, we can

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ion

10−2 10−1 100

Probability of false alarm

BCEDMMEEMEED

ED-0.5 dBED-1 dBED-1.5 dBED-2 dB

Figure 1: ROC curve: i.i.d source signal.

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BCEDMMEEMEED

ED-0.5 dBED-1 dBED-1.5 dBED-2 dB

Figure 2: ROC curve: wireless microphone source signal.

compare TBCED and TED with the minimum eigenvalue ofthe sample covariance matrix, resulting in the maximumto minimum eigenvalue (MME) detection and energy tominimum eigenvalue (EME) detection, respectively [21, 22].These methods can also be used for the single-antenna caseif signal samples are time-correlated [22].

Figures 1 and 2 show the Receiver Operating Charac-teristics (ROC) curves (Pd versus Pf a) at SNR = −15 dB,N = 5000, M = 4, and K = 1. In Figure 1, the sourcesignal is i.i.d and the flat-fading channel is assumed, whilein Figure 2, the source signal is the wireless microphonesignal [61, 65] and the multipath fading channel (with eight

EURASIP Journal on Advances in Signal Processing 9

independent taps of equal power) is assumed. For Figure 2,in order to exploit the correlation of signal samples in bothspace and time, the received signal samples are stacked as in(27). In both figures, “ED-x dB” means the energy detectionwith x-dB noise uncertainty. Note that both BCED and EDuse the true noise power to set the test threshold, whileMME and EME only use the estimated noise power as theminimum eigenvalue of the sample covariance matrix. It isobserved that for both cases of i.i.d source (Figure 1) andcorrelated source (Figure 2), BCED performs better than ED,and so does MME than EME. Comparing Figures 1 and 2, wesee that BCED and MME work better for correlated sourcesignals, while the reverse is true for ED and EME. It is alsoobserved that the performance of ED degrades dramaticallywhen there is noise power uncertainty.

10. Detection Threshold and TestStatistic Distribution

To make a decision on whether signal is present, we need toset a threshold γ for each proposed test statistic, such thatcertain Pd and/or Pf a can be achieved. For a fixed samplesize N , we cannot set the threshold to meet the targets forarbitrarily high Pd and low Pf a at the same time, as theyare conflicting to each other. Since we have little or no priorinformation on the signal (actually we even do not knowwhether there is a signal or not), it is difficult to set thethreshold based on Pd. Hence, a common practice is tochoose the threshold based on Pf a under hypothesis H0.

Without loss of generality, the test threshold can bedecomposed into the following form: γ = γ1T0(x), where γ1

is related to the sample size N and the target Pf a, and T0(x)is a statistic related to the noise distribution under H0. Forexample, for the energy detection with known noise power,we have

T0(x) = σ2η . (40)

For the matched-filtering detection with known noise power,we have

T0(x) = ση. (41)

For the EME/MME detection with no knowledge on thenoise power, we have

T0(x) = λmin(N), (42)

where λmin(N) is the minimum eigenvalue of the samplecovariance matrix. For the CAV detection, we can set

T0(x) = 1ML

ML∑

n=1

|rnn(N)|. (43)

In practice, the parameter γ1 can be set either empiricallybased on the observations over a period of time when thesignal is known to be absent, or analytically based on thedistribution of the test statistic under H0. In general, suchdistributions are difficult to find, while some known resultsare given as follows.

For energy detection defined in (8), it can be shown thatfor a sufficiently large values of N , its test statistic can be wellapproximated by the Gaussian distribution, that is,

1NM

TED(x) ∼ N

(σ2η ,

2σ4η

NM

)under H0. (44)

Accordingly, for given Pf a and N , the corresponding γ1 canbe found as

γ1 = NM

⎛⎝√

2NM

Q−1(Pf a)

+ 1

⎞⎠, (45)

where

Q(t) = 1√2π

∫ +∞

te−u

2/2du. (46)

For the matched-filtering detection defined in (9), for asufficiently large N , we have

1√∑N−1n=0 ‖s(n)‖2

TMF(x) ∼ N(

0, σ2η

)under H0. (47)

Thereby, for given Pf a and N , it can be shown that

γ1 = Q−1(Pf a)√√√√√N−1∑

n=0

‖s(n)‖2. (48)

For the GLRT-based detection, it can be shown that theasymptotic (as N → ∞) log-likelihood ratio is central chi-square distributed [13]. More precisely,

2 lnTGLRT(x) ∼ χ2r under H0, (49)

where r is the number of independent scalar unknownsunder H0 and H1. For instance, if σ2

η is known while Rs isnot, r will be equal to the number of independent real-valuedscalar variables in Rs. However, there is no explicit expressionfor γ1 in this case.

Random matrix theory (RMT) is useful for determiningthe test statistic distribution and the parameter γ1 forthe class of eigenvalue-based detection methods. In thefollowing, we provide an example for the BCED detectionmethod with known noise power, that is, T0(x) = σ2

η . Forthis method, we actually compare the ratio of the maximumeigenvalue of the sample covariance matrix Rx(N) to thenoise power σ2

η with a threshold γ1. To set the value for γ1, we

need to know the distribution of λmax(N)/σ2η for any finiteN .

With a finite N , Rx(N) may be very different from the actualcovariance matrix Rx due to the noise. In fact, characterizingthe eigenvalue distributions for Rx(N) is a very complicatedproblem [66–69], which also makes the choice of γ1 difficultin general.

When there is no signal, Rx(N) reduces to Rη(N), whichis the sample covariance matrix of the noise only. It is knownthat Rη(N) is a Wishart random matrix [66]. The studyof the eigenvalue distributions for random matrices is a

10 EURASIP Journal on Advances in Signal Processing

very hot research topic over recent years in mathematics,communications engineering, and physics. The joint PDF ofthe ordered eigenvalues of a Wishart random matrix has beenknown for many years [66]. However, since the expressionof the joint PDF is very complicated, no simple closed-formexpressions have been found for the marginal PDFs of theordered eigenvalues, although some computable expressionshave been found in [70]. Recently, Johnstone and Johanssonhave found the distribution of the largest eigenvalue [67, 68]of a Wishart random matrix as described in the followingtheorem.

Theorem 1. Let A(N)= (N/σ2η )Rη(N), μ= (

√N−1+

√M)

2,

and ν = (√N − 1 +

√M)(1/

√N − 1 + 1/

√M)

1/3. Assume that

limN→∞(M/N) = y (0 < y < 1). Then, (λmax(A(N)) −μ)/ν converges (with probability one) to the Tracy-Widomdistribution of order 1 [71, 72].

The Tracy-Widom distribution provides the limiting lawfor the largest eigenvalue of certain random matrices [71,72]. Let F1 be the cumulative distribution function (CDF)of the Tracy-Widom distribution of order 1. We have

F1(t) = exp(−1

2

∫∞

t

(q(u) + (u− t)q2(u)

)du)

, (50)

where q(u) is the solution of the nonlinear Painleve IIdifferential equation given by

q′′(u) = uq(u) + 2q3(u). (51)

Accordingly, numerical solutions can be found for functionF1(t) at different values of t. Also, there have been tables forvalues of F1(t) [67] and Matlab codes to compute them [73].

Based on the above results, the probability of false alarmfor the BCED detection can be obtained as

Pf a = P(λmax(N) > γ1σ

2η

)

= P

(σ2η

Nλmax(A(N)) > γ1σ

2η

)

= P(λmax(A(N)) > γ1N

)

= P

(λmax(A(N))− μ

ν>γ1N − μ

ν

)

≈ 1− F1

(γ1N − μ

ν

),

(52)

which leads to

F1

(γ1N − μ

ν

)≈ 1− Pf a (53)

or equivalently,

γ1N − μν

≈ F−11

(1− Pf a

). (54)

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alar

m

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1/threshold

Theoretical P f aActual P f a

Figure 3: Comparison of theoretical and actual Pf a.

From the definitions of μ and ν in Theorem 1, we finallyobtain the value for γ1 as

γ1 ≈(√

N +√M)2

N

×

⎛⎜⎝1 +

(√N +

√M)−2/3

(NM)1/6 F−11

(1− Pf a

)⎞⎟⎠.

(55)

Note that γ1 depends only on N and Pf a. A similar approachlike the above can be used for the case of MME detection, asshown in [21, 22].

Figure 3 shows the expected (theoretical) and actual (bysimulation) probability of false alarm values based on thetheoretical threshold in (55) for N = 5000, M = 8, andK = 1. It is observed that the differences between these twosets of values are reasonably small, suggesting that the choiceof the theoretical threshold is quite accurate.

11. Robust Spectrum Sensing

In many detection applications, the knowledge of signaland/or noise is limited, incomplete, or imprecise. This isespecially true in cognitive radio systems, where the primaryusers usually do not cooperate with the secondary usersand as a result the wireless propagation channels betweenthe primary and secondary users are hard to be predictedor estimated. Moreover, intentional or unintentional inter-ference is very common in wireless communications suchthat the resulting noise distribution becomes unpredictable.Suppose that a detector is designed for specific signal andnoise distributions. A pertinent question is then as follows:how sensitive is the performance of the detector to the errorsin signal and/or noise distributions? In many situations,the designed detector based on the nominal assumptionsmay suffer a drastic degradation in performance even with

EURASIP Journal on Advances in Signal Processing 11

small deviations from the assumptions. Consequently, thesearching for robust detection methods has been of greatinterest in the field of signal processing and many others [74–77]. A very useful paradigm to design robust detectors is themaxmin approach, which maximizes the worst case detectionperformance. Among others, two techniques are very usefulfor robust cognitive radio spectrum sensing: the robusthypothesis testing [75] and the robust matched filtering[76, 77]. In the following, we will give a brief overviewon them, while for other robust detection techniques, theinterested readers may refer to the excellent survey paper [78]and references therein.

11.1. Robust Hypothesis Testing. Let the PDF of a receivedsignal sample be f1 at hypothesis H1 and f0 at hypothesisH0. If we know these two functions, the LRT-based detectiondescribed in Section 2 is optimal. However, in practice, dueto channel impairment, noise uncertainty, and interference,it is very hard, if possible, to obtain these two functionsexactly. One possible situation is when we only know that f1and f0 belong to certain classes. One such class is called theε-contamination class given by

H0 : f0 ∈ F0, F0 ={

(1− ε0) f 00 + ε0g0

},

H1 : f1 ∈ F1, F1 ={

(1− ε1) f 01 + ε1g1

},

(56)

where f 0j ( j = 0, 1) is the nominal PDF under hypothesis H j ,

ε j in [0, 1] is the maximum degree of contamination, and gjis an arbitrary density function. Assume that we only knowf 0j and ε j (an upper bound for contamination), j = 1, 2. The

problem is then to design a detection scheme to minimizethe worst-case probability of error (e.g., probability of falsealarm plus probability of mis-detection), that is, finding adetector Ψ such that

Ψ=arg minΨ

max( f0, f1)∈F0×F1

(Pf a(f0, f1,Ψ

)+ 1−Pd

(f0, f1,Ψ

)).

(57)

Hubber [75] proved that the optimal test statistic is a“censored” version of the LRT given by

Ψ = TCLRT(x) =N−1∏

n=0

r(x(n)), (58)

where

r(t) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

c1, c1 ≤f 01 (t)

f 00 (t)

,

f 01 (t)

f 00 (t)

, c0 <f 01 (t)

f 00 (t)

,< c1

c0,f 01 (t)

f 00 (t)

≤ c0,

(59)

and c0, c1 are nonnegative numbers related to ε0, ε1, f 00 , and

f 01 [75, 78]. Note that if choosing c0 = 0 and c1 = +∞, the

test is the conventional LRT with respect to nominal PDFs,f 00 and f 0

1 .

After this seminal work, there have been quite a fewresearches in this area [78]. For example, similar minmaxsolutions are found for some other uncertainty models [78].

11.2. Robust Matched Filtering. We turn the model (4) into avector form as

H0 : x = η,

H1 : x = s + η,(60)

where s is the signal vector and η is the noise vector. Supposethat s is known. In general, a matched-filtering detectionis TMF = gTx. Let the covariance matrix of the noise beRη = E(ηηT). If Rη = σ2

η I, it is known that choosing g = sis optimal. In general, it is easy to verify that the optimal g tomaximize the SNR is

g = R−1η s. (61)

In practice, the signal vector s may not be known exactly. Forexample, s may be only known to be around s0 with someerrors modeled by

‖s− s0‖≤ Δ, (62)

where Δ is an upper bound on the Euclidean-norm of theerror. In this case, we are interested in finding a proper valuefor g such that the worst-case SNR is maximized, that is,

g = arg maxg

mins:||s−s0||≤Δ

SNR(

s, g). (63)

It was proved in [76, 77] that the optimal solution for theabove maxmin problem is

g =(

Rη + δI)−1

s0, (64)

where δ is a nonnegative number such that δ2‖g‖2 = Δ.It is noted that there are also researches on the robust

matched filtering detection when the signal has other typesof uncertainty [78]. Moreover, if the noise has uncertainties,that is, Rη is not known exactly, or both noise and signal haveuncertainties, the optimal robust matched-filtering detectorwas also found for some specific uncertainty models in [78].

12. Practical Considerations andFuture Developments

Although there have been quite a few methods proposedfor spectrum sensing, their realization and performance inpractical cognitive radio applications need to be tested [50–52]. To build a practical sensing device, many factors shouldbe considered. Some of them are discussed as follows.

(1) Narrowband noise. One or more narrowband filtersmay be used to extract the signal from a specific band. Thesefilters can be analog or digital. Only if the filter is ideallydesigned and the signal is critically sampled (sampling rateis the same as the bandwidth of the filter), the discrete noisesamples could be i.i.d. In a practical device, however, the

12 EURASIP Journal on Advances in Signal Processing

noise samples are usually correlated. This will cause manysensing methods unworkable, because they usually assumethat the noise samples are i.i.d. For some methods, a noiseprewhitening process can be used to make the noise samplesi.i.d. prior to the signal detection. For example, this methodhas been deployed in [22] to enable the eigenvalue-baseddetection methods. The similar method can be used forcovariance-based detection methods, for example, the CAV.

(2) Spurious signal and interference. The received signalmay contain not only the desired signal and white noise butalso some spurious signal and interference. The spurioussignal may be generated by Analog-to-Digital Convert-ers (ADC) due to its nonlinearity [79] or other inten-tional/unintentional transmitters. If the sensing antenna isnear some electronic devices, the spurious signal generatedby the devices can be strong in the received signal. For somesensing methods, such unwanted signals will be detected assignals rather than noise. This will increase the probabilityof false alarm. There are methods to mitigate the spurioussignal at the device level [79]. Alternatively, signal processingtechniques can be used to eliminate the impact of spurioussignal/interference [53]. It is very difficult, if possible, toestimate the interference waveform or distribution becauseof its variation with time and location. Depending onsituations, the interference power could be lower or higherthan the noise power. If the interference power is muchhigher than the noise power, it is possible to estimate theinterference first and subtract it from the received signal.However, since we usually intend to detect signal at verylow SNR, the error of the interference estimation could belarge enough (say, larger than the primary signal) such thatthe detection with the residue signal after the interferencesubtraction is still unreliable. If the interference power islow, it is hard to estimate it anyway. Hence, in general wecannot rely on the interference estimation and subtraction,especially for very low-power signal detection.

(3) Fixed point realization. Many hardware realizationsuse fixed point rather than floating point computation. Thiswill limit the accuracy of detection methods due to the signaltruncation when it is saturated. A detection method shouldbe robust to such unpredictable errors.

(4) Wideband sensing. A cognitive radio device mayneed to monitor a very large contiguous or noncontiguousfrequency range to find the best available band(s) fortransmission. The aggregate bandwidth could be as largeas several GHz. Such wideband sensing requires ultra-wide band RF frontend and very fast signal processingdevices. To sense a very large frequency range, typicallya corresponding large sampling rate is required, which isvery challenging for practical implementation. Fortunately,if a large part of the frequency range is vacant, that is, thesignal is frequency-domain sparse, we can use the recentlydeveloped compressed sampling (also called compressedsensing) to reduce the sampling rate by a large margin[80–82]. Although there have been studies in widebandsensing algorithms [26, 83–87], more researches are neededespecially when the center frequencies and bandwidths of theprimary signals are unknown within the frequency range ofinterest.

(5) Complexity. This is of course one of the major factorsaffecting the implementation of a sensing method. Simplebut effective methods are always preferable.

To detect a desired signal at very low SNR and in a harshenvironment is by no means a simple task. In this paper,major attention is paid to the statistical detection methods.The major advantage of such methods is their little depen-dency on signal/channel knowledge as well as relative ease forrealization. However, their disadvantage is also obvious: theyare in general vulnerable to undesired interferences. How wecan effectively combine the statistical detection with knownsignal features is not yet well understood. This might bea promising research direction. Furthermore, most exitingspectrum sensing methods are passive in the sense that theyhave neglected the interactions between the primary andsecondary networks via their mutual interferences. If thereaction of the primary user (e.g., power control) uponreceiving the secondary interference is exploited, some activespectrum sensing methods can be designed, which couldsignificantly outperform the conventional passive sensingmethods [88, 89]. At last, detecting the presence of signal isonly the basic task of sensing. For a radio with high levelof cognition, further information such as signal waveformand modulation schemes may be exploited. Therefore, signalidentification turns to be an advanced task of sensing. If wecould find an effective method for this advanced task, it inturn can help the basic sensing task.

13. Conclusion

In this paper, various spectrum sensing techniques have beenreviewed. Special attention has been paid to blind sensingmethods that do not need information of the source signalsand the propagation channels. It has been shown that space-time joint signal processing not only improves the sensingperformance but also solves the noise uncertainty problem tosome extent. Theoretical analysis on test statistic distributionand threshold setting has also been investigated.

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Photograph © Turisme de Barcelona / J. Trullàs

Preliminary call for papers

The 2011 European Signal Processing Conference (EUSIPCO 2011) is thenineteenth in a series of conferences promoted by the European Association forSignal Processing (EURASIP, www.eurasip.org). This year edition will take placein Barcelona, capital city of Catalonia (Spain), and will be jointly organized by theCentre Tecnològic de Telecomunicacions de Catalunya (CTTC) and theUniversitat Politècnica de Catalunya (UPC).EUSIPCO 2011 will focus on key aspects of signal processing theory and

li ti li t d b l A t f b i i ill b b d lit

Organizing Committee

Honorary ChairMiguel A. Lagunas (CTTC)

General ChairAna I. Pérez Neira (UPC)

General Vice ChairCarles Antón Haro (CTTC)

Technical Program ChairXavier Mestre (CTTC)

Technical Program Co Chairsapplications as listed below. Acceptance of submissions will be based on quality,relevance and originality. Accepted papers will be published in the EUSIPCOproceedings and presented during the conference. Paper submissions, proposalsfor tutorials and proposals for special sessions are invited in, but not limited to,the following areas of interest.

Areas of Interest

• Audio and electro acoustics.• Design, implementation, and applications of signal processing systems.

l d l d d

Technical Program Co ChairsJavier Hernando (UPC)Montserrat Pardàs (UPC)

Plenary TalksFerran Marqués (UPC)Yonina Eldar (Technion)

Special SessionsIgnacio Santamaría (Unversidadde Cantabria)Mats Bengtsson (KTH)

FinancesMontserrat Nájar (UPC)• Multimedia signal processing and coding.

• Image and multidimensional signal processing.• Signal detection and estimation.• Sensor array and multi channel signal processing.• Sensor fusion in networked systems.• Signal processing for communications.• Medical imaging and image analysis.• Non stationary, non linear and non Gaussian signal processing.

Submissions

Montserrat Nájar (UPC)

TutorialsDaniel P. Palomar(Hong Kong UST)Beatrice Pesquet Popescu (ENST)

PublicityStephan Pfletschinger (CTTC)Mònica Navarro (CTTC)

PublicationsAntonio Pascual (UPC)Carles Fernández (CTTC)

I d i l Li i & E hibiSubmissions

Procedures to submit a paper and proposals for special sessions and tutorials willbe detailed at www.eusipco2011.org. Submitted papers must be camera ready, nomore than 5 pages long, and conforming to the standard specified on theEUSIPCO 2011 web site. First authors who are registered students can participatein the best student paper competition.

Important Deadlines:

P l f i l i 15 D 2010

Industrial Liaison & ExhibitsAngeliki Alexiou(University of Piraeus)Albert Sitjà (CTTC)

International LiaisonJu Liu (Shandong University China)Jinhong Yuan (UNSW Australia)Tamas Sziranyi (SZTAKI Hungary)Rich Stern (CMU USA)Ricardo L. de Queiroz (UNB Brazil)

Webpage: www.eusipco2011.org

Proposals for special sessions 15 Dec 2010Proposals for tutorials 18 Feb 2011Electronic submission of full papers 21 Feb 2011Notification of acceptance 23 May 2011Submission of camera ready papers 6 Jun 2011